Answer:
a)
A={RRR,SSS,LLL}
b)
B={RSL,SLR,LRS,RLS,SRL,LSR}
c)
C={RRL,RLR,LRR,RRS,SRR,RSR}
d)
D={RRL, RRS, RLR, RLL, RSR, RSS, LRR, LRL, LLR, LLS, LSL, LSS, SRR, SRS, SLL, SLS, SSR, SSL}
e)
D'={RRR, RLS, RSL, LRS, LLL, LSR, SRL, SLR, SSS}
Step-by-step explanation:
Sample space=S= {RRR, RRL, RRS, RLR, RLL, RLS, RSR, RSL, RSS, LRR, LRL, LRS, LLR, LLL, LLS, LSR, LSL, LSS, SRR, SRL, SRS, SLR, SLL, SLS, SSR, SSL, SSS}
a)
Let A be the event that all three vehicles go in same direction. It means that the all three vehicles go to right or left or straight. Thus, event A can be represented as
A={RRR,SSS,LLL}
b)
Let B be the event that all three vehicles go in different direction. It means that the three vehicles can go to
1. Right, Straight, Left
2. Straight, Left, Right
3. Left, Right, Straight
4. Right, Left, Straight
5. Straight, Right, Left
6. Left, Straight, Right
Thus, event B can be represented as
B={RSL,SLR,LRS,RLS,SRL,LSR}
c)
Let C be the event that exactly two of three vehicles turn right. It means that the three vehicles can go to
1. Right, Right , Left
2. Right , Left, Right
3. Left, Right, Right
4. Right, Right , Straight
5. Straight, Right,Right
6. Right , Straight, Right
Thus, event C can be represented as
C={RRL,RLR,LRR,RRS,SRR,RSR}
d)
Let D be the event that exactly two of three vehicles go in same direction. It means that the three vehicles can go to
1. Right, Right, Left
2. Right, Right, Straight
3. Right, Left, Right
4. Right, Left, Left
5. Right, Straight, Right
6. Right, Straight, Straight
7. Left, Right, Right
8. Left, Right, Left
9. Left, Left, Right
10. Left, Left, Straight
11. Left, Straight, Left
12. Left, Straight, Straight
13. Straight, Right, Right
14. Straight, Right, Straight
15. Straight, Left, Left
16. Straight, Left, Straight
17. Straight, Straight, Right
18.Straight,Straight, Left
Thus, event D can be represented as
D={RRL, RRS, RLR, RLL, RSR, RSS, LRR, LRL, LLR, LLS, LSL, LSS, SRR, SRS, SLL, SLS, SSR, SSL}
e)
D'=S-D= {RRR, RRL, RRS, RLR, RLL, RLS, RSR, RSL, RSS, LRR, LRL, LRS, LLR, LLL, LLS, LSR, LSL, LSS, SRR, SRL, SRS, SLR, SLL, SLS, SSR, SSL, SSS} -{RRL, RRS, RLR, RLL, RSR, RSS, LRR, LRL, LLR, LLS, LSL, LSS, SRR, SRS, SLL, SLS, SSR, SSL}
D'={RRR, RLS, RSL, LRS, LLL, LSR, SRL, SLR, SSS}
